JEE Mains Laws of Motion
Q1. A block of mass 1 kg moving along x-axis with speed 10 m/s enters a rough region where the retarding force is F
r = −k·x N, with k = 10 N/m. The region ranges from x = 0.1 m to x = 1.9 m. Find the final speed of the block as it crosses the region.
- 4 m/s
- 10 m/s
- 6 m/s
- None of these
Q2. A body of mass m is suspended by two strings making angles θ₁ and θ₂ with the ceiling having tensions T₁ and T₂. If T₁ = √3 T₂, find θ₁ and θ₂.
- θ₁ = 30°, θ₂ = 60°, T₂ = 3mg/4
- θ₁ = 45°, θ₂ = 45°, T₂ = 3mg/4
- θ₁ = 30°, θ₂ = 60°, T₂ = 4mg/5
- None of these
Q3. A cubic block of mass m is sliding down a smooth plane inclined at 60° with acceleration g/2. The coefficient of kinetic friction is:
- √3/2
- √2/3
- 1 − √3/2
- √3 − 1
Q4. A light string passing over a smooth pulley connects two blocks of masses m₁ and m₂ (m₂ > m₁). If acceleration = g/√2, find m₁/m₂.
- (1 + √5)/(√5 − 1)
- (√2 − 1)/(√2 + 1)
- (√3 + 1)/(√2 − 1)
- None of these
Q5. A player caught a cricket ball of mass 150 g moving at 20 m/s. If the catching process is completed in 0.1 s, find the force exerted on the player’s hand.
- 150 N
- 30 N
- 300 N
- None of these
Q6. A light inextensible string passes over a smooth pulley connecting two blocks of masses m₁ and m₂. If acceleration = g/8, find ratio m₂/m₁.
Q7. Consider a block–trolley system where friction coefficient μ = 0.04, mass of trolley = 20 kg, hanging block = 6 kg. Find acceleration of the system.
Q8. The velocity of a particle of mass 500 g is given as v = (2t î + 3t² ĵ) m/s. If at t = 1 s, force = (î + x ĵ) N, find x.
Q9. The position vector of a particle at time t is r = (10t î + 15t² ĵ + 7k̂) m. The direction of net force on the particle is:
- Positive x-axis
- Positive y-axis
- Positive z-axis
- In x–y plane
Q10. The time taken by an object to slide down a 45° rough incline is n times that on a smooth 45° incline. The coefficient of friction is:
- 1 − 1/n²
- 1 + 1/n²
- √(1 − 1/n²)
- None of these
Quick Theory – Laws of Motion
- Newton’s 1st Law: A body remains in uniform motion unless acted upon by an external force.
- Newton’s 2nd Law: F = ma. Force is rate of change of momentum.
- Newton’s 3rd Law: For every action, there is an equal and opposite reaction.
- Tension in Strings: Same in all parts if string is light and frictionless pulley.
- Friction: f = μN; kinetic friction acts opposite to direction of motion.
- Equilibrium: ΣFx = 0, ΣFy = 0 for static conditions.